Read value from an fcurve at specific frames
I think this will do what you're asking:

object.animation_data.action.fcurves[1].evaluate(7)


In this example, fcurves1 would access the Y location curve in the collection of fcurves belonging to 'object'. And the Evaluate function will return the value of fcurves1 at frame 7.

This question has a more thorough answer.